Question: Simplify the following expression: $ q = \dfrac{-9}{8} + \dfrac{5r}{-r - 5} $
Solution: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-r - 5}{-r - 5}$ $ \dfrac{-9}{8} \times \dfrac{-r - 5}{-r - 5} = \dfrac{9r + 45}{-8r - 40} $ Multiply the second expression by $\dfrac{8}{8}$ $ \dfrac{5r}{-r - 5} \times \dfrac{8}{8} = \dfrac{40r}{-8r - 40} $ Therefore $ q = \dfrac{9r + 45}{-8r - 40} + \dfrac{40r}{-8r - 40} $ Now the expressions have the same denominator we can simply add the numerators: $q = \dfrac{9r + 45 + 40r}{-8r - 40} $ $q = \dfrac{49r + 45}{-8r - 40}$ Simplify the expression by dividing the numerator and denominator by -1: $q = \dfrac{-49r - 45}{8r + 40}$